Question

An airplane has wings, each with area A, designed so that air flows over the top of the wing at 265 m/s and underneath the wing at 234 m/s. If the mass of the airplane is 7.2×10^3 kg then what is the area of each wing needed to produce enough lift? (air = 1.29 kg/m^3 )

Answer 1

given,

Pressure on the top wing = 265 m/s

speed of underneath wings = 234 m/s

mass of the airplane = 7.2 × 10³ kg

density of air = 1.29 kg/m³

using Bernoulli's equation

`P_1 + (1)/(2)\rho v_1^2 = P_2 + (1)/(2)\rho v_2^2`

`\Delta P =(1)/(2)\rho (v_2^2-v_1^2)`

`\Delta P =(1)/(2)* 1.29* (265^2-234^2)`

`\Delta P =9977.5 Pa`

Applying newtons second law

2 Δ P x A - mg = 0

`A =(mg)/(2\Delta P)`

`A =(7.2* 10^3 * 9.8)/(2* 9977.5)`

A = 3.53 m²